Floating point arithmetic often requires alignment of the binary point of two numbers before operation. The exponent of the two numbers is compared to determine how much of a shift is needed to align the binary points. The mantissa of the smallest number is right shifted a number of places equal to the difference between the exponent of the greatest number and the exponent of the smallest number. This shift aligns the binary points of the number and permits addition or subtraction. The shift also loses some of the least significant bits of the smallest number, which are shifted out.
Following the arithmetic operation the result is rounded. The IEEE-754 floating point specification defines four rounding modes: 1) round towards positive infinity; 2) round towards negative infinity; 3) round towards the nearest integer; and round toward zero, also known as truncation. In the first three of these modes, the rounding may depend upon whether any of the shifted out least significant bits of the smallest number were 1. This is known as the sticky bit. It is known in the art to view these bits as they are shifted out during the shift operation. This permits detection of whether one or more of these bits is 1. This technique is relatively disadvantageous because it requires the complete shift to take place before the sticky bit is known. It would be advantageous if there were a faster method for determining if one of more of these shifted out least significant bits were 1.